Actually, I think countably infinite sets of sets are okay, too. It's when you're allowed to choose an arbitrary element from an uncountably infinite number of

Actually, I think countably infinite sets of sets are okay, too. It's when you're allowed to choose an arbitrary element from an uncountably infinite number of sets that weird things start happening. (Not that I can call pedantery given the sheer number of who-cares-about-the-details glosses in my original comment ;) And I don't know that I'd call infinity dangerous so much as I'd call it sanity-stretchingly counterintuitive. Which makes sense, really. Where would we have developed intuitions for dealing with the infinite?